Maria Miller apologises to MPs following the report into her expenses claims Credit: ITN Pool

In a letter to Scotland Yard, Thomas Docherty points out that the Parliamentary Commissioner for Standards said the Culture Secretary overclaimed by more than £40,000, but a committee of MPs reached a figure of £5,800, the sum which Mrs Miller has agreed to repay.

"Given the widely differing conclusions of the Commission and the Committee...I believe this matter warrants further investigation," Mr Docherty writes.